The present invention relates to communication systems and in particular to baseband signal processing in the receiving parts of base stations and mobile stations. The present invention provides a filter design method using spectral factorization that has a low complexity in implementation of the filter.
The cellular telephone industry has made phenomenal strides in commercial operations in the United States as well as the rest of the world. Growth in major metropolitan areas has far exceeded expectations and is rapidly outstripping system capacity. If this trend continues, the effects of this industry""s growth will soon reach even the smallest markets. Innovative solutions are required to meet these increasing capacity needs as well as maintain high quality service and avoid rising prices.
In mobile communication, the transmitted signal is often subjected to a time smearing effect created by the time dispersive nature of the channel, i.e., the air interface between a base station and a mobile station. The channel is estimated in the receiver part of a communication system, and used by the detector to aid in attempting to correctly deduce the information symbols that were transmitted thereto. A commonly used technique for deducing such received information symbols is Maximum Likelihood Sequence Estimation (MLSE) which, implemented using the Viterbi algorithm, is optimal for situations involving Additive White Gaussian Noise (AWGN).
Although the MLSE can be implemented through a computationally efficient Viterbi scheme, the MLSE might nonetheless be very computationally complex if large symbol alphabets are employed or if the number of required taps in the channel estimate is large. In order to reduce the complexity of the Viterbi part of the equalizer, decision feedback can be used. In a Decision Feedback Sequence Estimator (DFSE) equalizer, the estimated channel impulse response is split into two parts. The part which contains the first filter taps is referred to as the MLSE part and the remainder is referred to as the Decision Feedback Estimator (DFE) part.
By implementing this hybrid MLSE/DFE structure, the computational complexity of the detector is reduced, but with some possible loss in performance compared to a pure MLSE detector implementation. If the energy of the channel is concentrated in the first channel taps, i.e. the MLSE part, then the performance loss is small. This can be accomplished by placing a prefilter in the receive signal processing chain. The purpose of the prefilter is to change the characteristic of the channel""s impulse response such that the first channel taps are as large as possible. Furthermore, the prefilter should not change the magnitude response of the channel, or color the noise.
Basically, several approaches have been proposed for constructing prefilters. A first approach to prefilter design employs Minimum Mean Square Error (MMSE) techniques. The MMSE prefilter design follows from the design of a pure Decision Feedback Equalizer (DFE). However, the complexity of the MMSE prefilter design is high. Furthermore, the MMSE prefilter may color the noise, making it undesirable as a prefilter for a hybrid MLSE/DFE equalizer since the Viterbi MLSE part is not optimal for signals impacted by colored noise.
Second, allpass filters have been used as prefilters so that the new channel estimate becomes a minimum phase filter. These kinds of prefilters have been designed using a root search algorithm. The root search algorithm consists of an exhaustive sequential search that identifies each root one at a time. For example, in a 7th order channel estimate, seven roots have to be estimated. The first root has to be found using an iterative search method (e.g., Newton Raphson, such as described in Chapter 7 of Sxc3x6derstrxc3x6m and Stoica, System Identification, Prentice Hall 1989). Next, the root search method performs long division of the channel estimate with the first root. Thus, a 6th order channel remains after the division. A new iterative search, but now based on this 6th order channel, results in a second root. The method continues the process of iterative search and long division until the channel is reduced to a 4th order system. Then, the remaining four roots can be found by closed form equations. After all the seven roots of the channel estimate are calculated, all roots which are outside the unit circle are mirrored inside the unit circle, which results in a set of seven roots inside the unit circle. Based on this set of roots inside the unit circle, a minimum phase channel is constructed. Also, a prefilter is constructed based on this set of roots. However, the indirect nature of the root search algorithm is computationally complex.
A third approach is described in an article (Gerstacker et al., xe2x80x9cAn Efficient Method for Prefilter Computation for Reduced-State Equalizationxe2x80x9d, Proceedings of the PIMRC 2000 conference, London, UK, Sep. 18-21, 2000) and related European Patent Application EP 1032170 A1. The third approach consists of calculating a two stage FIR prefilter. The first FIR filter is a matched filter, i.e., the estimated channel conjugated and reversed. The second FIR filter consists of (a FIR approximation of) the inverse of the minimum phase version of the channel filter, which is also conjugated and reversed. The latter FIR filter is calculated from the solution of a set of Yule-Walker equations. This approach is more sensitive to truncation in the FIR approximations due to the two stage filtering, compared to the method described in the present document. Additionally, in section three of the article the authors detail other approaches that have lead to unsatisfactory solutions due to computational complexity. Among these other approaches is a spectral factorization technique which uses the cepstrum of the channel autocorrelation sequence. The authors note that the computational complexity is quite high and requires extensive logarithmic and exponential operations.
A spectral factorization technique which does not use the cepstrum is described in an article by Jezek, J., and Kucera, V., xe2x80x9cEfficient Algorithm for Matrix Spectral Factorizationxe2x80x9d, Automatica, Vol. 21, No. 6, pp. 663-669, 1985. However, this method is designed for real valued filter coefficients and does not allow for complex valued filter coefficients.
Thus, it would be desirable to generate new prefilter designs which are low in complexity, which do not color the noise, and which are implemented in a single stage while at the same time concentrating signal energy in the MLSE taps of the detector.
It should be emphasized that the terms xe2x80x9ccomprisesxe2x80x9d and xe2x80x9ccomprisingxe2x80x9d, when used in this specification, are taken to specify the presence of stated features, integers, steps or components; but the use of these terms does not preclude the presence or addition of one or more other features, integers, steps, components or groups thereof.
The present invention describes a spectral factorization method that is a low complexity alternative way of constructing prefilters, requiring a fraction of the computational complexity compared to conventional prefilter designs. Furthermore, the prefilter design of the present invention does not color the signal noise and operates as an allpass filter and can be realized in a single stage. Still further, the required program memory is significantly reduced by the spectral factorization method that does not involve using the cepstrum of the channel autocorrelation sequence or require extensive logarithmic and exponential operations. The spectral factorization method also is less sensitive to quantization noise in signals and channel estimates. Additionally, the invention describes how to construct prefilters to be used for equalization in both the forward and backward direction.
The present invention overcomes the computational complexity and inefficiency of the root search algorithm by directly calculating a minimum phase version, G(z), of a channel estimate, H(z) and calculating the prefilter from the minimum phase. One exemplary method provides for determining filter coefficients in a communication system by estimating a channel over which signals have been transmitted and determining the filter coefficients for a filter from the channel estimator using a spectral factorization method. Another exemplary method begins by initializing coefficients of the minimum phase filter, g, to coefficients of a spectrum of a channel estimate, s, wherein each coefficient numbers from 0 to L. An outer iterative loop starts by calculating a division factor, xcex30, from a complex conjugate of a first coefficient of the minimum phase filter G(z). The outer iterative loop starts by calculating a next Lth coefficient, XL, of the minimum phase filter by multiplying the Lth term of the spectrum with the division factor. A value m (starting at m=Lxe2x88x921) of an inner iterative counter is used and the next mth coefficient, xm, is calculated by an equation as follows:       x    m    =            (                        s          m                -                              ∑                          i              =                              m                +                1                                      L                    ⁢                      xe2x80x83                    ⁢                                    x              i                        ⁢                          g                              i                -                m                            *                                          )        ⁢          γ      0      
wherein g* is the complex conjugate of g. The value m is checked to see if m is equal to zero. If m is not zero, the value m is decreased by one and the process loops back to the start of the inner iterative loop. If m is equal to zero, the coefficients of the minimum phase filter, g, are set equal to the next coefficients of the minimum phase filter, x, for each coefficient from 0 to L. An outer iterative loop criteria is then checked. If the outer iterative loop criteria is met the process ends. If the outer iterative loop criteria is not met the process loops back to the start of the outer iterative loop.
The above features and advantages of the present invention will be more apparent and additional features and advantages of the present invention will be appreciated from the following detailed description of the invention made with reference to the drawings.